... to the variational statement leading to the Ritz-type analysis and involving the first derivatives. Therefore, except for special cases that may derive from specific and/or atypical complexities present in the Euler–Bernoulli beam systems, a Ritz-type analysis generally requires the use of class C 1 GPSFs (Fig...

... aiming piezoelectric motors applications have been modeled before in the literature [ 6 , 7 ] by using Euler–Bernoulli beam theory. They have limited applicability since the wavelength must be significantly larger than the beam thickness (as a characteristic length for the cross-section), which occurs...

... online January 16, 2014. Assoc. Editor: Dr. Corina Sandu. 26 03 2013 22 11 2013 This paper clarifies the reason why error occurs in the mass lumping procedure and presents a new approach to construct lumped mass matrices for Euler–Bernoulli beam elements, which contain both...

... of subsonic and supersonic loads. This is achieved by a suitable expansion in polynomial ratios of the Laplace transform, before going back to the original Fourier transform, whose inverse is obtained by exact calculations of the integrals over the complex infinite domain. For the Euler-Bernoulli beam...

... actuating forces/moments, in comparison with the asymptotic stabilizing BC law presented in Ref. 1 . Lotfazar , A. , Eghtesad , M. , and Najafi , A. , 2008 , “ Vibration Control and Trajectory Tracking for General In-Plane Motion of an Euler–Bernoulli Beam Via Two-Time Scale...

... controller provides very good trajectory tracking with acceptable actuating forces/moments. beams (structures) boundary-value problems vibration control vibration control two-time scale boundary control Euler–Bernoulli beam trajectory tracking PDE based systems Many manufacturing...